Analysis of Laminated Sandwich Plates Based on Interlaminar Shear Stress Continuous Plate Theory

The bending response of sandwich plates with stiff laminated face sheets is studied by a six-noded triangular element having seven degrees of freedom at each node. The element formulation is based on a refined higher-order plate theory having all the features for an accurate modeling of sandwich plates with affordable unknowns. The refined plate theory is quite attractive but suffers from a problem concerned with an interelement continuity requirement when it is used in finite element analysis. The problem has been dealt satisfactorily in this new element, which is applied to the analysis of sandwich plates of different kinds.     

Thermal Postbuckling of Laminated Composite Plates with Temperature Dependent Properties

The paper deals with the theoretical investigation of the postbuckling of laminated composite rectangular plates subjected to uniform in-plane temperature. An analytical method based on Chebyshev polynomial is employed. The formulation is based on Reissner–Mindlin plate theory and von Kármán nonlinear kinematics. The resulting nonlinear coupled differential equations are linearized using quadratic extrapolation technique. Double Chebyshev finite series is used to discretize the differential equations. An incremental iterative approach is employed for the solution. The effects of temperature dependent mechanical and thermal properties on the limiting/critical temperature and the postbuckling response are studied. The numerical results for different boundary conditions and lamination schemes are presented. Analysis results indicate that temperature dependent properties reduce the critical/limiting temperature and postbuckling strength.     

Postbuckling of Shear Deformable Laminated Cylindrical Shells

A postbuckling analysis is presented for a shear deformable laminated cylindrical shell of finite length subjected to compressive axial loads. The governing equations are based on Reddy’s higher-order shear deformation shell theory with a von Kármán–Donnell type of kinematic nonlinearity. The nonlinear prebuckling deformations and initial geometric imperfections of the shell are both taken into account. A boundary layer theory of shell buckling, which includes the effects of nonlinear prebuckling deformations, large deflections in the postbuckling range, and initial geometric imperfections of the shell, is extended to the case of shear deformable laminated cylindrical shells under axial compression. A singular perturbation technique is employed to determine the buckling loads and postbuckling equilibrium paths. The numerical illustrations concern the postbuckling response of perfect and imperfect, unstiffened or stiffened, moderately thick, cross-ply laminated cylindrical shells. The effects of transverse shear deformation, shell geometric parameters, total number of plies, fiber orientation, and initial geometric imperfections are studied.     

Thermomechanical Postbuckling of Cross-Ply Laminated Rectangular Plates

Postbuckling analysis is presented for shear deformable cross-ply laminated composite rectangular plates subjected to the combination of in-plane edge compressive mechanical loading and thermal loads due to a linearly varying temperature across the thickness. The formulation is based on the first-order shear deformation theory and von-Karman-type nonlinearity. The analysis uses a quadratic extrapolation technique for linearization and Chebyshev polynomials for spatial discretization. An incremental iterative approach is employed to estimate the critical load. The boundary conditions consisting of clamped, simply supported, free edge, and their combinations are considered. The effects of the thinness ratio, aspect ratio, lamination scheme, the number of layers, and the modulus ratio on the critical load/limit load and postbuckling behavior are studied.     

Buckling of Laminated Composite Rectangular Plates

The present study estimates the critical/buckling loads of laminated composite rectangular plates under in-plane uniaxial and biaxial loadings. The formulation is based on the first-order shear deformation theory and von-Karman-type nonlinearity. Chebyshev series is used for spatial discretisation and quadratic extrapolation is used for linearization. An incremental iterative approach is used for estimation of the critical load. Different combinations of simply supported, clamped and free boundary conditions are considered. The effects of plate aspect ratio, lamination scheme, number of layers and material properties on the critical loads are studied.     

Analysis of Hybrid Laminated Composite Plates

Hybrid laminated composite plates are analyzed using a nine‐noded isoparametric plate finite element based on Mindlin's theory. The shear flexibility is included in the finite element modeling. Shear flexibility is of importance, especially when different materials are used in the laminate design. Hybrid laminates consisting of graphite∕epoxy and kevlar∕epoxy plies are considered for illustration. The study indicates that hybrid laminates provide stiffnesses that are intermediate to the values obtained for single‐material laminates. The minimum deflection is achieved at different fiber orientation for thick plates compared to thin plates. The deflection behavior of hybrid laminates seems to be less affected by outer‐ply stiffness in the case of thick plates. Thick plates show less variation in the first natural frequency with fiber orientation but hybridization changes the natural frequency considerably. The first natural frequency of the hybrid laminate can be made higher than the stiffer single‐material laminate.     

Bounds on Flexural Properties and Buckling Response for Symmetrically Laminated Composite Plates

Nondimensional parameters and equations governing the buckling behavior of rectangular symmetrically laminated plates are presented that can be used to represent the buckling resistance, for plates made of all known structural materials, in a very general, insightful, and encompassing manner. In addition, these parameters can be used to assess the degree of plate orthotropy, to assess the importance of anisotropy that couples bending and twisting deformations, and to characterize quasi-isotropic laminates quantitatively. Bounds for these nondimensional parameters are also presented that are based on thermodynamics and practical laminate construction considerations. These bounds provide insight into potential gains in buckling resistance through laminate tailoring and composite-material development. As an illustration of this point, upper bounds on the buckling resistance of long rectangular orthotropic plates with simply supported or clamped edges and subjected to uniform axial compression, uniform shear, or pure in-plane bending loads are presented. The results indicate that the maximum gain in buckling resistance for tailored orthotropic laminates, with respect to the corresponding isotropic plate, is in the range of 26–36% for plates with simply supported edges, irrespective of the loading conditions. For the plates with clamped edges, the corresponding gains in buckling resistance are in the range of 9–12% for plates subjected to compression or pure in-plane bending loads and potentially up to 30% for plates subjected to shear loads.     

Natural Vibrations of Laminated and Sandwich Plates

An exact analytical solution based on the propagator matrix method and a semianalytical solution based on a higher-order mixed approach (displacement and stress interpolation) have been presented in this paper to evaluate the natural frequencies as well as the stress and displacement mode shapes of simply supported, cross-ply laminated and sandwich plates. Continuity of the transverse stresses and displacements has been maintained at the laminae interfaces. Results have been presented for orthotropic plates, symmetric as well as nonsymmetric cross-ply composite and sandwich laminates. Results from the propagator matrix agree well with the published results for frequencies as well as displacement and stress mode shapes. Furthermore, the frequencies and displacement and stress eigenvectors obtained from the proposed layerwise mixed method are in excellent agreement with those obtained by three-dimensional elasticity theory. Results obtained from the present equivalent single layer theory are in good agreement with those obtained from the displacement based higher order methods. The high accuracy of the present methods is further confirmed by comparing the response of a sandwich plate with significantly different layer properties for which the conventional displacement based formulations yield inaccurate solutions.     

Free-Vibration Analysis and Material Constants Identification of Laminated Composite Sandwich Plates

Free vibration of symmetrically laminated composite sandwich plates with elastic edge restraints is studied via the Rayleigh–Ritz approach. The proposed Rayleigh–Ritz method is constructed on the basis of the layer-wise linear displacement theory. The accuracy of the method in predicting natural frequencies of composite sandwich plates with different boundary conditions is verified by the results reported in the literature or the experimental data obtained in this study. The proposed method is then applied to the material constant identification of free composite sandwich plates using the first six theoretical natural frequencies of the plates. In the identification process, trial material constants are used in the present method to predict the theoretical natural frequencies, a frequency discrepancy function is established to measure the sum of the squared differences between the experimental and theoretical natural frequencies, and a stochastic global minimization algorithm is used to search for the best estimates of the material constants by making the frequency discrepancy function a global minimum. Applications of the material constant identification technique are demonstrated by means of several examples.     

Analysis of Thick Circular Plates Undergoing Large Deflections

This investigation considers the effect of transverse shear deformation on bending of the axisymmetrically loaded isotropic and orthotropic circular and annular plates undergoing large deflection. The analysis treats the nonlinear terms of lateral displacement as fictitious loads acting on the plate. The solution of a von Kármán‐type plate is, therefore, reduced to a plane problem in elasticity and a linear plate‐bending problem. Results are presented for simply supported and clamped plates and are in good agreement with the available solutions. For plates considered in this study, the influence of shear deformation on lateral displacement becomes more significant as the orthotropic parameter increases. The linear and nonlinear solutions for orthotropic plates deviate at a low value of the maximum deflection‐to‐thickness ratio (w/h). Consequently, the extent of w/h within which the small‐deflection theory is applicable to orthotropic plates is much lower than the value of about 0.4 typically used for isotropic plates, and it depends, in general, on the degree of orthotropy. The technique employed in this study is well suited for the analysis of nonlinear plate problems.     

Plastic-Buckling of Rectangular Plates under Combined Uniaxial and Shear Stresses

This paper is concerned with the plastic-buckling of rectangular plates under uniaxial compressive and shear stresses. In the prediction of the plastic-buckling stresses, we have adopted the incremental theory of plasticity for capturing the inelastic behavior, the Mindlin plate theory for the effect of transverse shear deformation, the Ramberg-Osgood stress–strain relation for the plate material, and the Ritz method for the bifurcation buckling analysis. The interaction curves of the plastic uniaxial buckling stress and the plastic shear buckling stress for thin and thick rectangular plates are presented for various aspect ratios. The effect of transverse shear deformation is examined by comparing the interaction curves obtained based on the Mindlin plate theory and the classical thin plate theory.     

Hygrothermoelastic Postbuckling Response of Laminated Composite Plates

The paper deals with the effect of moisture and temperature on the postbuckling response of a laminated composite plate subjected to hygrothermomechanical loadings. Mechanical loading consists of uniaxial, biaxial, shear, and their combinations. The distribution of temperature and moisture on the surface is considered to be uniform. The degradation in material properties due to moisture and temperature is taken into account using a micromechanical model. The mathematical formulation is based on higher order shear deformation theory and von Karman’s nonlinear kinematics. The quadratic extrapolation technique and fast converging finite double Chebyshev series are used for linearization and spatial discretization of the governing nonlinear equations of equilibrium, respectively. The effects of temperature rise, moisture concentration, fiber-volume fraction, and plate parameters on buckling and postbuckling response of the plate are presented.     

Influence of Shear Deformation on Buckling of Pultruded Fiber Reinforced Plastic Profiles

Theoretical studies of the influence of shear deformation on the flexural, torsional, and lateral buckling of pultruded fiber reinforced plastic (FRP)-I-profiles are presented. Theoretical developments are based on the governing energy equations and full section member properties. The solution for flexural buckling is consistent with the established solution based on the governing differential equation. The new solutions for torsional and lateral buckling incorporate a reduction factor similar to that for flexural buckling. The solution for lateral buckling also incorporates the influence of prebuckling displacements. Closed form solutions for a series of simply supported, pultruded FRP I-profiles, based on experimentally determined full section flexural and torsional properties, indicate the following conclusions. For members subjected to axial compression, shear deformation can reduce the elastic flexural and torsional buckling loads by up to approximately 15% and 10%, respectively. For members subjected to bending, prebuckling displacements can increase the buckling moments by over 20% while shear deformation decreases the buckling moments by less than 5%.     

Fracture Analysis of Shear Deformable Bi-Material Interface

Based on a novel split bi-layer shear deformable beam model capable of capturing the local deformation at the crack tip, the explicit closed-form solutions of bi-material interface fracture are presented in this paper. A recently developed novel shear deformable bi-layer beam theory is briefly reviewed, from which the deformation at the crack tip is explicitly derived. A new expression for the energy release rate is then obtained using the J integral, in which several new terms associated with the transverse shear force are present; this represents an improved solution compared to the one from the classical beam model. By exploiting the two concentrated crack tip forces, the general loadings acting at the crack tip are decomposed into two groups which produce only the mode I and mode II energy release rates, respectively; the total energy release rate is thus decomposed into the mode I and II components in a global sense. The stress intensity factor referred to as local decomposition is also obtained including the transverse shear effect. The difference between the global and local mode decompositions is clarified, and a simple relationship between them is provided. The effect of the existence of a thin layer of adhesive on the stress intensity factor is further studied by an asymptotic analysis. A simple and improved expression for the T stress, the nonsingular term of stress at the crack tip, is also given. The fracture parameters of several commonly used interface fracture specimens are summarized. The present fracture analysis including the transverse shear effect is in better agreement with finite element analyses and shows advantages and improved accuracy over the available classical solutions.     

Buckling of Circular Mindlin Plates with an Internal Ring Support and Elastically Restrained Edge

This paper is concerned with the elastic buckling problem of circular Mindlin plates with a concentric internal ring support and elastically restrained edge. In solving this problem analytically, the circular plate is first divided into an annular segment and a core circular segment at the location of the internal ring support. Based on the Mindlin plate theory, the governing differential equations for the annular and circular segments are then solved exactly and the solutions brought together by using the interfacial conditions. New exact critical buckling loads of circular Mindlin plate with an internal ring support and elastically restrained edge are presented for the first time. The optimal radius of the internal ring support for maximum buckling load is also found. An approximate relationship between the buckling loads of such circular plates based on the classical thin plate theory and the Mindlin plate theory is also explored.     

Delamination Effect on Flutter of Homogeneous Laminated Plates

The effect of delamination on the flutter boundary of two‐dimensional laminated plates are investigated theoretically. Linear‐plate theory and qusai‐steady aerodynamic theory are employed. A simple beam‐plate‐theory model is developed to predict the flutter boundaries of delaminated homogeneous plates with simply supported ends. The effects of delamination position, size, and thickness on the flutter boundary are studied in detail. The results reveal that the presence of a delamination degraded the stiffness and the natural frequencies of the plate and thereby decreases the flutter boundary of the plate. However, for certain geometries the flutter boundaries were raised due to the flutter coalescence modes of the plate altered by the presence of a delamination in the plate.     

Local Buckling of Elastically Restrained Fiber-Reinforced Plastic Plates and its Application to Box Sections

An analytical study of local buckling of rectangular composite plates rotationally restrained elastically along unloaded edges and subjected to nonuniform in-plane axial action at simply supported loaded edges is presented. A variational formulation of the Ritz method is used to establish an eigenvalue problem, and by using combined harmonic and polynomial buckling deformation functions, which satisfy all the restrained boundary conditions, the explicit solution of plate local buckling coefficients is obtained. The explicit formulas for local buckling strength of orthotropic plates are simplified to the cases of isotropic plates, which are consistent with classical solutions. The elastically rotationally restrained plates are further treated as discrete plates or panels of fiber-reinforced plastic (FRP) box shapes, and by considering the effect of elastic restraints at the joint connections of flanges and webs, the local buckling strength of FRP box shapes is predicted. The theoretical predictions are in good agreement with transcendental solutions and finite-element eigenvalue analyses for local buckling of FRP box columns. The present explicit formulation can be applied to determine local buckling capacities of composite plates with elastic restraints along the unloaded edges and can be further used to predict the local buckling strength of FRP shapes.     

E-Glass/Vinylester Composites in Aqueous Environments: Effects on Short-Beam Shear Strength

The paper present the results of extended (225 weeks) aqueous immersion of E-glass/vinylester composites, fabricated by the resin infusion process. Two different architectures (unidirectional and bidirectional) are tested to assess effects of temperature levels between 5 and 60°C on the short-beam shear strength. Tests show the competing effects of plasticization and postcuring balanced by hydrolytic degradation. The maximum reduction in performance is seen through immersion in deionized water at 60°C wherein pronounced interface and fiber level degradation is noted. Cycling between the two extremes of 5 and 60°C is also seen to cause acceleration of some interface and bulk resin related degradation phenomena. Experimental results obtained from hygrothermal aging at 23°C are compared with predictions based on an Arrhenius type model, and it is shown that good correlation can be obtained in sets where degradation mechanisms remain the same. Shortcomings of this type of model for life predictions are discussed to emphasize viability of use in design.     

System Identification of Partially Restrained Composite Plates Using Measured Natural Frequencies

A nondestructive evaluation technique established on the basis of a global minimization method is presented for the system identification of laminated composite plates partially restrained by elastic edge supports. Six natural frequencies extracted from the vibration data of the flexibly restrained plate are used to identify the system parameters of the plate. In the identification process, the trial system parameters are used in the Rayleigh–Ritz method to predict the theoretical natural frequencies of the plate, an error function is established to measure the sum of the differences between the experimental and theoretical predictions of the natural frequencies, and the global minimization method is used to search for the best estimates of the parameters by making the error function a global minimum. The accuracy and efficiency of the proposed technique in identifying the parameters of several flexibly supported plates made of different composite materials are studied via both theoretical and experimental approaches. The excellent results obtained in this study have validated the applicability of the proposed technique.     

Repair of Steel Composite Beams with Carbon Fiber-Reinforced Polymer Plates

One significant cause of deterioration of steel bridge structures is the corrosion due to extensive use of deicing salts in winter weather. The investigation presented in this paper focused on the behavior of steel composite beams damaged intentionally at their tension flange to simulate corrosion and then repaired with carbon fiber-reinforced polymer (CFRP) plates attached to their tension areas side. Damage to the beams was induced by removing part of the bottom flange, which was varied between no damage and loss of 75% of the bottom flange. All beams were tested to failure to observe their behavior in the elastic, inelastic, and ultimate states. To help implement this strengthening technique, a nonlinear analytical procedure was also developed to predict the behavior of the section/member in the elastic, inelastic, and ultimate states. The test results showed a significant increase in the strength and stiffness of the repaired beams. Through the use of CFRP plates, all damaged beams were fully restored to their original (undamaged state) strength.